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A comprehensive and user-friendly introduction to statistics-now revised and updated Introductory Statistics for the Behavioral Sciences has had a long and successful history and is a popular and well-respected statistics text. Now in its sixth edition, the text has been thoroughly revised to present all the topics students in the behavioral sciences need in a uniquely accessible format that aids in the comprehension and implementation of the statistical analyses most commonly used in the behavioral sciences. Using a continuous narrative that explains statistics and tracks a common data set throughout, the authors have developed an innovative approach that makes the material unintimidating and memorable, providing a framework that connects all of the topics in the text and allows for easy comparison of different statistical analyses. New features in this Sixth Edition include: * Different aspects of a common data set are used to illustrate the various statistical methods throughout the text, with an emphasis on drawing connections between seemingly disparate statistical procedures and formulas * Computer exercises based on the same large data set and relevant to that chapter's content. The data set can be analyzed by any available statistical software * New "Bridge to SPSS" sections at the end of each chapter explain, for those using this very popular statistical package, how to perform that chapter's statistical procedures by computer, and how to translate the output from SPSS * New chapters on multiple comparisons and repeated-measures ANOVA

Joan Welkowitz, PhD, was a Professor of Psychology at New York University. She directed the clinical program for ten years, and taught courses in methodology and statistics at both the graduate and undergraduate levels for more than twenty-five years.

Barry H. Cohen, PhD, is the Director of the master's program in psychology at New York University, where he has been teaching statistics for more than twenty years. He is the author or coauthor of two other successful statistics books also from Wiley–Explaining Psychological Statistics, Second Edition and Essentials of Statistics for the Social and Behavioral Sciences with R. Brooke Lea.

Robert B. Ewen, PhD, teaches advanced placement psychology at Gulliver Preparatory School in Miami, Florida. He previously taught statistics for eight years as an associate professor at New York University. He is also the author of a successful college text on theories of personality that is currently in its sixth edition.

Preface

xv

Acknowledgments

xix

Glossary of Symbols

xxi

Part I Descriptive Statistics

1

(122)

Introduction

3

(20)

Why Study Statistics?

4

(1)

Descriptive and Inferential Statistics

5

(1)

Populations, Samples, Parameters, and Statistics

6

(1)

Measurement Scales

6

(2)

Independent and Dependent Variables

8

(1)

Sara's Study

9

(1)

Summation Notation

10

(6)

Summary

16

(1)

Exercises

17

(3)

Thought Questions

20

(1)

Computer Exercises

21

(1)

Bridge to SPSS

21

(2)

Frequency Distributions and Graphs

23

(19)

The Purpose of Descriptive Statistics

24

(1)

Regular Frequency Distributions

25

(1)

Cumulative Frequency Distributions

26

(1)

Grouped Frequency Distributions

27

(3)

Graphic Representations

30

(5)

Shapes of Frequency Distributions

35

(2)

Summary

37

(1)

Exercises

38

(1)

Thought Questions

39

(1)

Computer Exercises

40

(1)

Bridge to SPSS

40

(2)

Transformed Scores I: Percentiles

42

(14)

Interpreting a Raw Score

43

(1)

Definition of Percentile and Percentile Rank

43

(1)

Computational Procedures

44

(8)

Deciles, Quartiles, and the Median

52

(1)

Summary

52

(1)

Exercises

53

(1)

Thought Questions

54

(1)

Computer Exercises

54

(1)

Bridge to SPSS

54

(2)

Measures of Central Tendency

56

(13)

Introduction

57

(1)

The Mean

58

(6)

The Median

64

(2)

The Mode

66

(1)

Summary

66

(1)

Exercises

67

(1)

Thought Questions

67

(1)

Computer Exercises

68

(1)

Bridge to SPSS

68

(1)

Measures of Variability

69

(16)

The Concept of Variability

70

(2)

The Range

72

(1)

The Semi-Interquartile Range

73

(1)

The Standard Deviation and Variance

74

(6)

Summary

80

(2)

Exercises

82

(1)

Thought Questions

83

(1)

Computer Exercises

83

(1)

Bridge to SPSS

84

(1)

Additional Techniques for Describing Batches of Data

85

(9)

Numerical Summaries

86

(2)

Graphic Summaries

88

(3)

Summary

91

(1)

Exercises

91

(1)

Thought Questions

92

(1)

Computer Exercises

92

(1)

Bridge to SPSS

92

(2)

Transformed Scores II: z and T Scores

94

(14)

Interpreting a Raw Score

95

(1)

Rules for Changing X and σ

96

(2)

Standard Scores (z Scores)

98

(2)

T Scores and SAT Scores

100

(2)

IQ Scores

102

(1)

Summary

103

(1)

Exercises

104

(2)

Thought Questions

106

(1)

Computer Exercises

106

(1)

Bridge to SPSS

106

(2)

The Normal Distribution

108

(15)

Introduction

109

(1)

Score Distributions

110

(1)

Parameters of the Normal Distribution

111

(1)

Tables of the Standard Normal Distribution

111

(1)

Characteristics of the Normal Curve

112

(1)

Illustrative Examples

113

(6)

Summary

119

(1)

Exercises

120

(1)

Thought Questions

121

(1)

Computer Exercises

121

(1)

Bridge to SPSS

121

(2)

Part II Basic Inferential Statistics

123

(164)

Introduction to Statistical Inference

125

(25)

Introduction

126

(1)

The Goals of Inferential Statistics

127

(1)

Sampling Distributions

128

(4)

The Standard Error of the Mean

132

(3)

The z Score for Sample Means

135

(2)

Null Hypothesis Testing

137

(7)

Assumptions Required by the Statistical Test for the Mean of a Single Population

144

(1)

Summary

144

(2)

Exercises

146

(2)

Thought Questions

148

(1)

Computer Exercises

149

(1)

Bridge to SPSS

149

(1)

The One-Sample t Test and Interval Estimation

150

(17)

The Statistical Test for the Mean of a Single Population When σ Is Not Known: The t Distributions

151

(4)

Interval Estimation

155

(4)

The Standard Error of a Proportion

159

(3)

Summary

162

(2)

Exercises

164

(1)

Thought Questions

165

(1)

Computer Exercises

166

(1)

Bridge to SPSS

166

(1)

Testing Hypotheses about the Difference between the Means of Two Populations

167

(30)

The Standard Error of the Difference

169

(4)

Estimating the Standard Error of the Difference

173

(1)

The t Test for Two Sample Means

174

(3)

Confidence Intervals for the Difference of Two Population Means

177

(2)

Using the t Test for Two Sample Means: Some General Considerations

179

(2)

Measuring Size of an Effect

181

(1)

The t Test for Matched Samples

182

(6)

Summary

188

(3)

Exercises

191

(2)

Thought Questions

193

(2)

Computer Exercises

195

(1)

Bridge to SPSS

195

(2)

Linear Correlation and Prediction

197

(44)

Introduction

198

(3)

Describing the Linear Relationship between Two Variables

201

(9)

Interpreting the Magnitude of a Pearson r

210

(2)

When Is It Important That Pearson's r be Large?

212

(2)

Testing the Significance of the Correlation Coefficient

214

(3)

Prediction and Linear Regression

217

(8)

Measuring Prediction Error: The Standard Error of Estimate

225

(3)

Summary

228

(2)

Exercises

230

(3)

Thought Questions

233

(1)

Computer Exercises

234

(1)

Bridge to SPSS

235

(1)

Appendix: Equivalence of the Various Formulas for r

236

(5)

The Connection between Correlation and the t Test

241

(14)

Introduction

242

(1)

The Point-Biserial Correlation Coefficient

243

(3)

The Proportion of Variance Accounted For in Your Samples

246

(1)

Estimating the Proportion of Variance Accounted For in the Population

247

(2)

Summary

249

(1)

Exercises

250

(1)

Thought Questions

251

(1)

Computer Exercises

252

(1)

Bridge to SPSS

252

(3)

Introduction to Power Analysis

255

(32)

Introduction

256

(1)

Concepts of Power Analysis

257

(2)

The Test of the Mean of a Single Population

259

(5)

The Significance Test of the Proportion of a Single Population

264

(2)

The Significance Test of a Pearson r

266

(1)

Testing the Difference between Independent Means

267

(5)

Testing the Difference between the Means of Two Matched Populations

272

(1)

Choosing a Value for d for a Power Analysis Involving Independent Means

273

(2)

Using Power Analysis to Interpret the Results of Null Hypothesis Tests

275

(2)

Summary

277

(4)

Exercises

281

(2)

Thought Questions

283

(1)

Computer Exercises

284

(1)

Bridge to SPSS

284

(3)

Part III Analysis of Variance Methods

287

(100)

One-Way Analysis of Variance

289

(25)

Introduction

290

(1)

The General Logic of ANOVA

291

(4)

Computational Procedures

295

(6)

Comparing the One-Way ANOVA with the t Test

301

(1)

A Simplified ANOVA Formula for Equal Sample Sizes

302

(3)

Effect Size for the One-Way ANOVA

305

(1)

Summary

306

(3)

Exercises

309

(1)

Thought Questions

310

(1)

Computer Exercises

311

(1)

Bridge to SPSS

312

(1)

Appendix: Proof That the Total Sum of Squares Is Equal to the Sum of the Between-Group and the Within-Group Sum of Squares

312

(2)

Multiple Comparisons

314

(18)

Introduction

315

(1)

Fisher's Protected t Tests

316

(3)

Tukey's Honestly Significant Difference (HSD)

319

(3)

Other Multiple Comparison Procedures

322

(2)

Planned and Complex Comparisons

324

(3)

Summary

327

(1)

Exercises

328

(1)

Thought Questions

329

(1)

Computer Exercises

330

(1)

Bridge to SPSS

330

(2)

Introduction to Factorial Design: Two-Way Analysis of Variance

332

(27)

Introduction

333

(1)

Computational Procedures

334

(8)

The Meaning of Interaction

342

(4)

Following Up a Significant Interaction

346

(3)

Summary

349

(3)

Exercises

352

(3)

Thought Questions

355

(1)

Computer Exercises

356

(2)

Bridge to SPSS

358

(1)

Repeated-Measures ANOVA

359

(28)

Introduction

360

(1)

Calculating the One-Way RM ANOVA

360

(3)

Rationale for the RM ANOVA Error Term

363

(2)

Assumptions of the RM ANOVA

365

(2)

The RM versus RB Design: An Introduction to Issues of Experimental Design

367

(4)

The Two-Way Mixed Design

371

(6)

Summary

377

(5)

Exercises

382

(2)

Thought Questions

384

(1)

Computer Exercises

384

(1)

Bridge to SPSS

384

(3)

Part IV Nonparametric Statistics

387

(78)

Introduction to Probability and Nonparametric Methods

389

(20)

Introduction

390

(1)

Probability

391

(3)

The Binomial Distribution

394

(6)

The Sign Test for Matched Samples

400

(2)

Summary

402

(1)

Exercises

403

(2)

Thought Questions

405

(1)

Computer Exercises

406

(1)

Bridge to SPSS

406

(3)

Chi Square Tests

409

(23)

Chi Square and Goodness of Fit: One-Variable Problems

410

(4)

Chi Square as a Test of Independence: Two-Variable Problems

414

(6)

Measures of Strength of Association in Two-Variable Tables

420

(3)

Summary

423

(2)

Exercises

425

(2)

Thought Questions

427

(1)

Computer Exercises

428

(1)

Bridge to SPSS

429

(3)

Tests for Ordinal Data

432

(33)

Introduction

433

(3)

The Difference between the Locations of Two Independent Samples: The Rank-Sum Test

436

(4)

Differences among the Locations of Two or More Independent Samples: The Kruskal-Wallis H Test

440

(4)

The Difference between the Locations of Two Matched Samples: The Wilcoxon Test

444

(5)

The Relationship between Two Ranked Variables: The Spearman Rank-Order Correlation